## Warning in strptime(x, format, tz = tz): unknown timezone 'zone/tz/2018g.
## 1.0/zoneinfo/America/Chicago'

In the videogame Player Unkown’s Battleground, players compete in a free for all battle arena that takes the form of a pair of islands surrounded by a vast ocean. Players are scattered throughout the island and must search the various buildings and facilities on the islands for weapons and gear that can be used to help survive the battle. Each player will have a rating based upon how well they do in a vareity of different aspects. The purpose of our analysis is to determine if there is a statistical correlation we can draw from this player data that will help us determine what seperates the different players in terms of solo rating.

Normalization of the data

We normalized the data to [0,1] range and plotted the normalized values against the original values to double check that normalization worked

Check the Distribution of each variable

Distribution of each variable with log transformation

vars: 2, 3, 4, & 7 appear to be normally distributed when log transformed

# There are 0.0000 values in ~200 cells of the 90000 element normalmatrix. Loss of data deemed acceptable.

Distribution of each variable with square root transformation

Vars: 5 & 6 look more normally distributed with square root transformation

Histograms of transformed variables

Summary of Multiple Regression for non-transformed variables

## 
## Call:
## lm(formula = solo_Rating ~ solo_WinRatio + solo_KillDeathRatio + 
##     solo_RoundsPlayed + solo_MoveDistancePg + solo_DamagePg + 
##     solo_KillsPg + solo_AvgSurvivalTime)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.09796 -0.10428 -0.00523  0.10475  0.49474 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           0.137655   0.006220  22.132  < 2e-16 ***
## solo_WinRatio         0.008555   0.021635   0.395  0.69255    
## solo_KillDeathRatio  -0.216838   0.077880  -2.784  0.00538 ** 
## solo_RoundsPlayed     1.633815   0.021805  74.930  < 2e-16 ***
## solo_MoveDistancePg   0.385274   0.019078  20.195  < 2e-16 ***
## solo_DamagePg         1.633649   0.108786  15.017  < 2e-16 ***
## solo_KillsPg         -1.629142   0.129539 -12.576  < 2e-16 ***
## solo_AvgSurvivalTime -0.007080   0.016339  -0.433  0.66480    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.146 on 9992 degrees of freedom
## Multiple R-squared:  0.3997, Adjusted R-squared:  0.3992 
## F-statistic: 950.3 on 7 and 9992 DF,  p-value: < 2.2e-16

First order model does not look very promising with an adjusted R-squared value of .3992. Future transformations will hopefully increase this value.

Correlation Matrix for non-transformed variables

##             track          var1        var2        var3       var4
## track  1.00000000 -0.0951925063 -0.06005138 -0.08659303 -0.0312682
## var1  -0.09519251  1.0000000000 -0.05658658 -0.07756071  0.5793137
## var2  -0.06005138 -0.0565865825  1.00000000  0.72561229 -0.1977646
## var3  -0.08659303 -0.0775607132  0.72561229  1.00000000 -0.2259784
## var4  -0.03126820  0.5793136992 -0.19776461 -0.22597835  1.0000000
## var5  -0.11741882  0.1261006396  0.37229531  0.35989254 -0.1607233
## var6  -0.11004922 -0.0469249397  0.63340017  0.88466753 -0.2457212
## var7  -0.09956666 -0.0773213629  0.65628540  0.90537805 -0.2562709
## var8  -0.08238990 -0.0004090853  0.45492268  0.43391719 -0.2418726
##             var5        var6        var7          var8
## track -0.1174188 -0.11004922 -0.09956666 -0.0823899021
## var1   0.1261006 -0.04692494 -0.07732136 -0.0004090853
## var2   0.3722953  0.63340017  0.65628540  0.4549226795
## var3   0.3598925  0.88466753  0.90537805  0.4339171887
## var4  -0.1607233 -0.24572117 -0.25627093 -0.2418725737
## var5   1.0000000  0.39692699  0.38475078  0.6791649776
## var6   0.3969270  1.00000000  0.98402862  0.4571464487
## var7   0.3847508  0.98402862  1.00000000  0.4546263913
## var8   0.6791650  0.45714645  0.45462639  1.0000000000

Scatter plot of solo_Rating vs each non-transformed variable

Summary of Multiple Regression for transformed variables

## 
## Call:
## lm(formula = solo_Rating.nrm ~ Log.solo_WinRatio.nrm + Log.solo_KillDeathRatio.nrm + 
##     Log.solo_RoundsPlayed.nrm + Sqrt.solo_MoveDistancePg.nrm + 
##     Sqrt.solo_DamagePg.nrm + Log.solo_KillsPg.nrm + solo_AvgSurvivalTime.nrm)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.49657 -0.05850 -0.00151  0.06496  0.30382 
## 
## Coefficients:
##                               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                   0.977309   0.054415  17.960   <2e-16 ***
## Log.solo_WinRatio.nrm         0.029172   0.002346  12.437   <2e-16 ***
## Log.solo_KillDeathRatio.nrm   0.038378   0.016327   2.351   0.0188 *  
## Log.solo_RoundsPlayed.nrm     0.154270   0.001602  96.316   <2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm  0.455743   0.017438  26.135   <2e-16 ***
## Sqrt.solo_DamagePg.nrm       -0.114415   0.066115  -1.731   0.0836 .  
## Log.solo_KillsPg.nrm          0.039482   0.016480   2.396   0.0166 *  
## solo_AvgSurvivalTime.nrm      0.136473   0.013821   9.874   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09482 on 6938 degrees of freedom
## Multiple R-squared:  0.6692, Adjusted R-squared:  0.6689 
## F-statistic:  2005 on 7 and 6938 DF,  p-value: < 2.2e-16

After several transofrmations on the predictors, our Adjusted R-squared is now sitting at a relatively pleasing .6689. Even further manipulation of the data may allow us to tweek this value a bit.

Dropping the least significant variable transmatrix Sqrt.solo_DamagePg.nrm.

Correlation Matrix for transformed variables

##                             tracktrans solo_rating.mtrx solo_WinRatio.mtrx
## tracktrans                 1.000000000      -0.08887507         -0.0893966
## solo_rating.mtrx          -0.088875073       1.00000000         -0.3274858
## solo_WinRatio.mtrx        -0.089396598      -0.32748579          1.0000000
## solo_KillDeathRatio.mtrx  -0.127687085      -0.22022057          0.7825900
## solo_RoundsPlayed.mtrx    -0.001660295       0.69172864         -0.7711185
## solo_MoveDistancePg.mtrx  -0.140201211       0.10881856          0.4806081
## solo_DamagePg.mtrx        -0.137925165      -0.16434659          0.7108651
## solo_KillsPg.mtrx         -0.134591260      -0.18225228          0.7298163
## solo_AvgSurvivalTime.mtrx -0.098855539      -0.04991211          0.5417566
##                           solo_KillDeathRatio.mtrx solo_RoundsPlayed.mtrx
## tracktrans                              -0.1276871           -0.001660295
## solo_rating.mtrx                        -0.2202206            0.691728639
## solo_WinRatio.mtrx                       0.7825900           -0.771118529
## solo_KillDeathRatio.mtrx                 1.0000000           -0.634358921
## solo_RoundsPlayed.mtrx                  -0.6343589            1.000000000
## solo_MoveDistancePg.mtrx                 0.3529028           -0.333226265
## solo_DamagePg.mtrx                       0.9722485           -0.560207655
## solo_KillsPg.mtrx                        0.9859195           -0.576510743
## solo_AvgSurvivalTime.mtrx                0.4258529           -0.455848539
##                           solo_MoveDistancePg.mtrx solo_DamagePg.mtrx
## tracktrans                              -0.1402012         -0.1379252
## solo_rating.mtrx                         0.1088186         -0.1643466
## solo_WinRatio.mtrx                       0.4806081          0.7108651
## solo_KillDeathRatio.mtrx                 0.3529028          0.9722485
## solo_RoundsPlayed.mtrx                  -0.3332263         -0.5602077
## solo_MoveDistancePg.mtrx                 1.0000000          0.3467629
## solo_DamagePg.mtrx                       0.3467629          1.0000000
## solo_KillsPg.mtrx                        0.3158699          0.9733448
## solo_AvgSurvivalTime.mtrx                0.6657312          0.3979725
##                           solo_KillsPg.mtrx solo_AvgSurvivalTime.mtrx
## tracktrans                       -0.1345913               -0.09885554
## solo_rating.mtrx                 -0.1822523               -0.04991211
## solo_WinRatio.mtrx                0.7298163                0.54175661
## solo_KillDeathRatio.mtrx          0.9859195                0.42585294
## solo_RoundsPlayed.mtrx           -0.5765107               -0.45584854
## solo_MoveDistancePg.mtrx          0.3158699                0.66573118
## solo_DamagePg.mtrx                0.9733448                0.39797252
## solo_KillsPg.mtrx                 1.0000000                0.37297388
## solo_AvgSurvivalTime.mtrx         0.3729739                1.00000000

curvilinear relationship between Win Ratio and KDR, solo_rating and Rounds Played. Clear patterns hard to distinquish via visual analysis alone. Further plotting and statistical analysis is required. # Scatter plot of solo_rating vs each transformed variable # MoveDistancePg has an odd shape due to the nature of the game. As some players will often die from the very ofset of the game in a Hunger Games-esque battle arena. # Normal Q-Q plots of the transformed data

## Warning in data.row.names(row.names, rowsi, i): some row.names duplicated:
## 2,3,4,5,6,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,28,29,30,31,32,33,34,35,36,38,39,40,41,42
## --> row.names NOT used
##    size       Cp    1     2    3    4    5    6     SSEp       AIC
## 37    6 8.315854 TRUE FALSE TRUE TRUE TRUE TRUE 62.43278 -32716.38
##         SBC
## 37 -32675.3

SBC criterion suggests that we disclude Log.solo_KillDeathRatio.nrm but retain the remaining predictors

## Warning: package 'corrplot' was built under R version 3.4.2
## corrplot 0.84 loaded
##                           solo_rating.mtrx solo_WinRatio.mtrx
## solo_rating.mtrx                      1.00              -0.33
## solo_WinRatio.mtrx                   -0.33               1.00
## solo_KillDeathRatio.mtrx             -0.22               0.78
## solo_RoundsPlayed.mtrx                0.69              -0.77
## solo_MoveDistancePg.mtrx              0.11               0.48
## solo_DamagePg.mtrx                   -0.16               0.71
## solo_KillsPg.mtrx                    -0.18               0.73
## solo_AvgSurvivalTime.mtrx            -0.05               0.54
##                           solo_KillDeathRatio.mtrx solo_RoundsPlayed.mtrx
## solo_rating.mtrx                             -0.22                   0.69
## solo_WinRatio.mtrx                            0.78                  -0.77
## solo_KillDeathRatio.mtrx                      1.00                  -0.63
## solo_RoundsPlayed.mtrx                       -0.63                   1.00
## solo_MoveDistancePg.mtrx                      0.35                  -0.33
## solo_DamagePg.mtrx                            0.97                  -0.56
## solo_KillsPg.mtrx                             0.99                  -0.58
## solo_AvgSurvivalTime.mtrx                     0.43                  -0.46
##                           solo_MoveDistancePg.mtrx solo_DamagePg.mtrx
## solo_rating.mtrx                              0.11              -0.16
## solo_WinRatio.mtrx                            0.48               0.71
## solo_KillDeathRatio.mtrx                      0.35               0.97
## solo_RoundsPlayed.mtrx                       -0.33              -0.56
## solo_MoveDistancePg.mtrx                      1.00               0.35
## solo_DamagePg.mtrx                            0.35               1.00
## solo_KillsPg.mtrx                             0.32               0.97
## solo_AvgSurvivalTime.mtrx                     0.67               0.40
##                           solo_KillsPg.mtrx solo_AvgSurvivalTime.mtrx
## solo_rating.mtrx                      -0.18                     -0.05
## solo_WinRatio.mtrx                     0.73                      0.54
## solo_KillDeathRatio.mtrx               0.99                      0.43
## solo_RoundsPlayed.mtrx                -0.58                     -0.46
## solo_MoveDistancePg.mtrx               0.32                      0.67
## solo_DamagePg.mtrx                     0.97                      0.40
## solo_KillsPg.mtrx                      1.00                      0.37
## solo_AvgSurvivalTime.mtrx              0.37                      1.00

## 
## Call:
## lm(formula = solo_Rating.nrm ~ Log.solo_WinRatio.nrm + Log.solo_KillDeathRatio.nrm + 
##     Log.solo_RoundsPlayed.nrm + Sqrt.solo_MoveDistancePg.nrm + 
##     Log.solo_KillsPg.nrm + solo_AvgSurvivalTime.nrm)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.49385 -0.05885 -0.00151  0.06497  0.30345 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  0.888112   0.017449  50.898   <2e-16 ***
## Log.solo_WinRatio.nrm        0.029981   0.002299  13.043   <2e-16 ***
## Log.solo_KillDeathRatio.nrm  0.027397   0.015045   1.821   0.0687 .  
## Log.solo_RoundsPlayed.nrm    0.154017   0.001595  96.546   <2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm 0.451722   0.017285  26.134   <2e-16 ***
## Log.solo_KillsPg.nrm         0.031619   0.015844   1.996   0.0460 *  
## solo_AvgSurvivalTime.nrm     0.135766   0.013817   9.826   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09483 on 6939 degrees of freedom
## Multiple R-squared:  0.6691, Adjusted R-squared:  0.6688 
## F-statistic:  2338 on 6 and 6939 DF,  p-value: < 2.2e-16

There appears to be a strong correlation between solo_rating and RoundsPlayed, KillDeathRatio and WinRatio,etc. With a strong negative correlation between WinRatio and RoundsPlayed, which makes complete sense give one of the two is a ratio between games won vs games played.The correlation between MoveDistance and SurvivalTime is expected as well, as not only are the players going to be alive if they are moving around, as the game progresses, the remaining players are forced ever closer together.

## Warning: package 'MASS' was built under R version 3.4.3

## Start:  AIC=-36299.62
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm + Log.solo_RoundsPlayed.nrm + 
##     Sqrt.solo_MoveDistancePg.nrm + Log.solo_KillsPg.nrm + solo_AvgSurvivalTime.nrm
## 
##                                Df Sum of Sq    RSS    AIC
## <none>                                      37.271 -36300
## - solo_AvgSurvivalTime.nrm      1     0.573 37.844 -36196
## - Log.solo_WinRatio.nrm         1     0.738 38.009 -36165
## - Log.solo_KillsPg.nrm          1     2.209 39.480 -35902
## - Sqrt.solo_MoveDistancePg.nrm  1     4.001 41.272 -35593
## - Log.solo_RoundsPlayed.nrm     1    55.307 92.578 -29982

## 
## Call:
## lm(formula = Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm + Log.solo_RoundsPlayed.nrm + 
##     Sqrt.solo_MoveDistancePg.nrm + Log.solo_KillsPg.nrm + solo_AvgSurvivalTime.nrm)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.49111 -0.04401  0.00321  0.05227  0.19546 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  0.990952   0.011267   87.95   <2e-16 ***
## Log.solo_WinRatio.nrm        0.019820   0.001691   11.72   <2e-16 ***
## Log.solo_RoundsPlayed.nrm    0.122650   0.001209  101.48   <2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm 0.364488   0.013354   27.30   <2e-16 ***
## Log.solo_KillsPg.nrm         0.053757   0.002650   20.28   <2e-16 ***
## solo_AvgSurvivalTime.nrm     0.108895   0.010543   10.33   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07328 on 6940 degrees of freedom
## Multiple R-squared:  0.6903, Adjusted R-squared:  0.6901 
## F-statistic:  3094 on 5 and 6940 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + 
##     Log.solo_RoundsPlayed.nrm.c + Log.solo_KillsPg.nrm.c + Sqrt.solo_DamagePg.nrm.c + 
##     Sqrt.solo_MoveDistancePg.nrm.c + solo_AvgSurvivalTime.nrm.c + 
##     Win.Rounds + Win.Kills + Win.Damage + Win.Move + Win.Time + 
##     Rounds.Kills + Rounds.Damage + Rounds.Move + Rounds.Time + 
##     Kills.Damage + Kills.Move + Kills.Time + Damage.Move + Damage.Time + 
##     Time.Move)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.46030 -0.04372  0.00304  0.05016  0.31231 
## 
## Coefficients: (1 not defined because of singularities)
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     0.6509609  0.0013419 485.110  < 2e-16 ***
## Log.solo_WinRatio.nrm.c         0.0202971  0.0017370  11.685  < 2e-16 ***
## Log.solo_RoundsPlayed.nrm.c     0.1207529  0.0013213  91.391  < 2e-16 ***
## Log.solo_KillsPg.nrm.c         -0.0010354  0.0129973  -0.080 0.936510    
## Sqrt.solo_DamagePg.nrm.c        0.3419275  0.0812903   4.206 2.63e-05 ***
## Sqrt.solo_MoveDistancePg.nrm.c  0.3985045  0.0138355  28.803  < 2e-16 ***
## solo_AvgSurvivalTime.nrm.c      0.1127655  0.0105687  10.670  < 2e-16 ***
## Win.Rounds                      0.0006582  0.0011383   0.578 0.563111    
## Win.Kills                      -0.0121923  0.0127992  -0.953 0.340833    
## Win.Damage                      0.1819949  0.0765381   2.378 0.017442 *  
## Win.Move                       -0.0662632  0.0186590  -3.551 0.000386 ***
## Win.Time                       -0.1178422  0.0890083  -1.324 0.185565    
## Rounds.Kills                    0.0013214  0.0113609   0.116 0.907408    
## Rounds.Damage                  -0.0445192  0.0631911  -0.705 0.481135    
## Rounds.Move                    -0.0058920  0.0142294  -0.414 0.678834    
## Rounds.Time                     0.0024845  0.0103755   0.239 0.810759    
## Kills.Damage                   -0.3353641  0.0313815 -10.687  < 2e-16 ***
## Kills.Move                     -0.2814325  0.1066222  -2.640 0.008321 ** 
## Kills.Time                             NA         NA      NA       NA    
## Damage.Move                     1.0027123  0.5846875   1.715 0.086398 .  
## Damage.Time                     0.5826874  0.4987769   1.168 0.242753    
## Time.Move                      -0.3919282  0.0965290  -4.060 4.96e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07149 on 6925 degrees of freedom
## Multiple R-squared:  0.7059, Adjusted R-squared:  0.7051 
## F-statistic: 831.1 on 20 and 6925 DF,  p-value: < 2.2e-16
## Start:  AIC=-36628.18
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Log.solo_KillsPg.nrm.c + Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage + 
##     Win.Move + Win.Time + Rounds.Kills + Rounds.Damage + Rounds.Move + 
##     Rounds.Time + Kills.Damage + Kills.Move + Kills.Time + Damage.Move + 
##     Damage.Time + Time.Move
## 
## 
## Step:  AIC=-36628.18
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Log.solo_KillsPg.nrm.c + Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage + 
##     Win.Move + Win.Time + Rounds.Kills + Rounds.Damage + Rounds.Move + 
##     Rounds.Time + Kills.Damage + Kills.Move + Damage.Move + Damage.Time + 
##     Time.Move
## 
##                                  Df Sum of Sq    RSS    AIC
## - Log.solo_KillsPg.nrm.c          1     0.000 35.396 -36630
## - Rounds.Kills                    1     0.000 35.396 -36630
## - Rounds.Time                     1     0.000 35.396 -36630
## - Rounds.Move                     1     0.001 35.397 -36630
## - Win.Rounds                      1     0.002 35.398 -36630
## - Rounds.Damage                   1     0.003 35.399 -36630
## - Win.Kills                       1     0.005 35.401 -36629
## - Damage.Time                     1     0.007 35.403 -36629
## - Win.Time                        1     0.009 35.405 -36628
## <none>                                        35.396 -36628
## - Damage.Move                     1     0.015 35.411 -36627
## - Win.Damage                      1     0.029 35.425 -36625
## - Kills.Move                      1     0.036 35.432 -36623
## - Win.Move                        1     0.064 35.460 -36618
## - Time.Move                       1     0.084 35.480 -36614
## - Sqrt.solo_DamagePg.nrm.c        1     0.090 35.486 -36612
## - solo_AvgSurvivalTime.nrm.c      1     0.582 35.978 -36517
## - Kills.Damage                    1     0.584 35.980 -36517
## - Log.solo_WinRatio.nrm.c         1     0.698 36.094 -36495
## - Sqrt.solo_MoveDistancePg.nrm.c  1     4.240 39.636 -35844
## - Log.solo_RoundsPlayed.nrm.c     1    42.692 78.088 -31134
## 
## Step:  AIC=-36630.17
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage + 
##     Win.Move + Win.Time + Rounds.Kills + Rounds.Damage + Rounds.Move + 
##     Rounds.Time + Kills.Damage + Kills.Move + Damage.Move + Damage.Time + 
##     Time.Move
## 
##                                  Df Sum of Sq    RSS    AIC
## - Rounds.Kills                    1     0.000 35.396 -36632
## - Rounds.Time                     1     0.000 35.396 -36632
## - Rounds.Move                     1     0.001 35.397 -36632
## - Win.Rounds                      1     0.002 35.398 -36632
## - Rounds.Damage                   1     0.003 35.399 -36632
## - Win.Kills                       1     0.005 35.401 -36631
## - Damage.Time                     1     0.007 35.403 -36631
## - Win.Time                        1     0.009 35.405 -36630
## <none>                                        35.396 -36630
## - Damage.Move                     1     0.015 35.411 -36629
## + Log.solo_KillsPg.nrm.c          1     0.000 35.396 -36628
## - Win.Damage                      1     0.029 35.425 -36627
## - Kills.Move                      1     0.036 35.432 -36625
## - Win.Move                        1     0.065 35.461 -36619
## - Time.Move                       1     0.084 35.480 -36616
## - solo_AvgSurvivalTime.nrm.c      1     0.582 35.978 -36519
## - Log.solo_WinRatio.nrm.c         1     0.708 36.104 -36495
## - Kills.Damage                    1     0.728 36.124 -36491
## - Sqrt.solo_DamagePg.nrm.c        1     1.636 37.032 -36318
## - Sqrt.solo_MoveDistancePg.nrm.c  1     4.369 39.765 -35824
## - Log.solo_RoundsPlayed.nrm.c     1    43.311 78.707 -31081
## 
## Step:  AIC=-36632.15
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage + 
##     Win.Move + Win.Time + Rounds.Damage + Rounds.Move + Rounds.Time + 
##     Kills.Damage + Kills.Move + Damage.Move + Damage.Time + Time.Move
## 
##                                  Df Sum of Sq    RSS    AIC
## - Rounds.Time                     1     0.000 35.396 -36634
## - Rounds.Move                     1     0.001 35.397 -36634
## - Win.Rounds                      1     0.002 35.398 -36634
## - Damage.Time                     1     0.008 35.404 -36633
## - Win.Time                        1     0.010 35.406 -36632
## <none>                                        35.396 -36632
## - Win.Kills                       1     0.014 35.411 -36631
## - Damage.Move                     1     0.015 35.411 -36631
## + Rounds.Kills                    1     0.000 35.396 -36630
## + Log.solo_KillsPg.nrm.c          1     0.000 35.396 -36630
## - Rounds.Damage                   1     0.029 35.425 -36628
## - Kills.Move                      1     0.036 35.432 -36627
## - Win.Damage                      1     0.063 35.459 -36622
## - Win.Move                        1     0.065 35.461 -36621
## - Time.Move                       1     0.084 35.481 -36618
## - solo_AvgSurvivalTime.nrm.c      1     0.583 35.979 -36521
## - Log.solo_WinRatio.nrm.c         1     0.709 36.105 -36496
## - Kills.Damage                    1     0.728 36.124 -36493
## - Sqrt.solo_DamagePg.nrm.c        1     1.649 37.045 -36318
## - Sqrt.solo_MoveDistancePg.nrm.c  1     4.370 39.766 -35826
## - Log.solo_RoundsPlayed.nrm.c     1    43.548 78.944 -31062
## 
## Step:  AIC=-36634.1
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage + 
##     Win.Move + Win.Time + Rounds.Damage + Rounds.Move + Kills.Damage + 
##     Kills.Move + Damage.Move + Damage.Time + Time.Move
## 
##                                  Df Sum of Sq    RSS    AIC
## - Rounds.Move                     1     0.001 35.397 -36636
## - Win.Rounds                      1     0.003 35.399 -36636
## - Damage.Time                     1     0.008 35.404 -36635
## <none>                                        35.396 -36634
## - Win.Time                        1     0.011 35.407 -36634
## - Win.Kills                       1     0.014 35.411 -36633
## - Damage.Move                     1     0.015 35.412 -36633
## + Rounds.Time                     1     0.000 35.396 -36632
## + Rounds.Kills                    1     0.000 35.396 -36632
## + Log.solo_KillsPg.nrm.c          1     0.000 35.396 -36632
## - Rounds.Damage                   1     0.029 35.426 -36630
## - Kills.Move                      1     0.035 35.432 -36629
## - Win.Damage                      1     0.063 35.460 -36624
## - Win.Move                        1     0.065 35.461 -36623
## - Time.Move                       1     0.088 35.484 -36619
## - solo_AvgSurvivalTime.nrm.c      1     0.583 35.979 -36523
## - Log.solo_WinRatio.nrm.c         1     0.709 36.105 -36498
## - Kills.Damage                    1     0.728 36.125 -36495
## - Sqrt.solo_DamagePg.nrm.c        1     1.651 37.047 -36319
## - Sqrt.solo_MoveDistancePg.nrm.c  1     4.372 39.768 -35827
## - Log.solo_RoundsPlayed.nrm.c     1    43.742 79.138 -31047
## 
## Step:  AIC=-36635.97
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage + 
##     Win.Move + Win.Time + Rounds.Damage + Kills.Damage + Kills.Move + 
##     Damage.Move + Damage.Time + Time.Move
## 
##                                  Df Sum of Sq    RSS    AIC
## - Win.Rounds                      1     0.002 35.399 -36638
## - Damage.Time                     1     0.008 35.405 -36636
## <none>                                        35.397 -36636
## - Win.Time                        1     0.011 35.408 -36636
## - Win.Kills                       1     0.014 35.411 -36635
## - Damage.Move                     1     0.016 35.413 -36635
## + Rounds.Move                     1     0.001 35.396 -36634
## + Rounds.Kills                    1     0.000 35.397 -36634
## + Log.solo_KillsPg.nrm.c          1     0.000 35.397 -36634
## + Rounds.Time                     1     0.000 35.397 -36634
## - Rounds.Damage                   1     0.032 35.429 -36632
## - Kills.Move                      1     0.036 35.433 -36631
## - Win.Damage                      1     0.063 35.460 -36626
## - Win.Move                        1     0.079 35.476 -36623
## - Time.Move                       1     0.088 35.485 -36621
## - solo_AvgSurvivalTime.nrm.c      1     0.585 35.982 -36524
## - Log.solo_WinRatio.nrm.c         1     0.714 36.111 -36499
## - Kills.Damage                    1     0.730 36.127 -36496
## - Sqrt.solo_DamagePg.nrm.c        1     1.664 37.061 -36319
## - Sqrt.solo_MoveDistancePg.nrm.c  1     4.372 39.769 -35829
## - Log.solo_RoundsPlayed.nrm.c     1    43.875 79.272 -31038
## 
## Step:  AIC=-36637.52
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move + 
##     Win.Time + Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move + 
##     Damage.Time + Time.Move
## 
##                                  Df Sum of Sq    RSS    AIC
## - Damage.Time                     1     0.008 35.407 -36638
## <none>                                        35.399 -36638
## - Win.Time                        1     0.011 35.411 -36637
## - Damage.Move                     1     0.015 35.415 -36637
## - Win.Kills                       1     0.017 35.416 -36636
## + Win.Rounds                      1     0.002 35.397 -36636
## + Rounds.Time                     1     0.001 35.399 -36636
## + Rounds.Kills                    1     0.000 35.399 -36636
## + Rounds.Move                     1     0.000 35.399 -36636
## + Log.solo_KillsPg.nrm.c          1     0.000 35.399 -36636
## - Rounds.Damage                   1     0.031 35.430 -36634
## - Kills.Move                      1     0.034 35.434 -36633
## - Win.Damage                      1     0.064 35.463 -36627
## - Time.Move                       1     0.087 35.487 -36622
## - Win.Move                        1     0.099 35.498 -36620
## - solo_AvgSurvivalTime.nrm.c      1     0.583 35.983 -36526
## - Log.solo_WinRatio.nrm.c         1     0.712 36.111 -36501
## - Kills.Damage                    1     0.736 36.136 -36496
## - Sqrt.solo_DamagePg.nrm.c        1     1.750 37.149 -36304
## - Sqrt.solo_MoveDistancePg.nrm.c  1     4.532 39.932 -35803
## - Log.solo_RoundsPlayed.nrm.c     1    49.083 84.483 -30598
## 
## Step:  AIC=-36637.93
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move + 
##     Win.Time + Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move + 
##     Time.Move
## 
##                                  Df Sum of Sq    RSS    AIC
## - Win.Time                        1     0.006 35.413 -36639
## <none>                                        35.407 -36638
## + Damage.Time                     1     0.008 35.399 -36638
## + Win.Rounds                      1     0.003 35.405 -36636
## + Rounds.Kills                    1     0.001 35.406 -36636
## + Rounds.Time                     1     0.001 35.407 -36636
## + Rounds.Move                     1     0.000 35.407 -36636
## + Log.solo_KillsPg.nrm.c          1     0.000 35.407 -36636
## - Rounds.Damage                   1     0.037 35.444 -36633
## - Win.Kills                       1     0.038 35.445 -36632
## - Damage.Move                     1     0.040 35.447 -36632
## - Kills.Move                      1     0.069 35.477 -36626
## - Time.Move                       1     0.082 35.490 -36624
## - Win.Damage                      1     0.102 35.510 -36620
## - Win.Move                        1     0.104 35.511 -36620
## - solo_AvgSurvivalTime.nrm.c      1     0.583 35.991 -36526
## - Log.solo_WinRatio.nrm.c         1     0.715 36.122 -36501
## - Kills.Damage                    1     0.743 36.150 -36496
## - Sqrt.solo_DamagePg.nrm.c        1     1.742 37.150 -36306
## - Sqrt.solo_MoveDistancePg.nrm.c  1     4.527 39.935 -35804
## - Log.solo_RoundsPlayed.nrm.c     1    49.150 84.557 -30593
## 
## Step:  AIC=-36638.79
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move + 
##     Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move + 
##     Time.Move
## 
##                                  Df Sum of Sq    RSS    AIC
## <none>                                        35.413 -36639
## + Win.Time                        1     0.006 35.407 -36638
## + Kills.Time                      1     0.006 35.407 -36638
## + Rounds.Time                     1     0.003 35.410 -36637
## + Win.Rounds                      1     0.003 35.410 -36637
## + Damage.Time                     1     0.003 35.411 -36637
## + Rounds.Kills                    1     0.001 35.412 -36637
## + Log.solo_KillsPg.nrm.c          1     0.000 35.413 -36637
## + Rounds.Move                     1     0.000 35.413 -36637
## - Rounds.Damage                   1     0.033 35.446 -36634
## - Win.Kills                       1     0.036 35.449 -36634
## - Damage.Move                     1     0.043 35.456 -36632
## - Kills.Move                      1     0.083 35.496 -36625
## - Win.Damage                      1     0.097 35.511 -36622
## - Time.Move                       1     0.099 35.512 -36621
## - Win.Move                        1     0.100 35.513 -36621
## - solo_AvgSurvivalTime.nrm.c      1     0.578 35.991 -36528
## - Log.solo_WinRatio.nrm.c         1     0.710 36.123 -36503
## - Kills.Damage                    1     0.737 36.151 -36498
## - Sqrt.solo_DamagePg.nrm.c        1     1.768 37.182 -36302
## - Sqrt.solo_MoveDistancePg.nrm.c  1     4.580 39.994 -35796
## - Log.solo_RoundsPlayed.nrm.c     1    49.151 84.564 -30595

The most significant interaction effects are WinRatio to MoveDistance, KillsPg to DamagePg, SurvivalTime To MoveDistance. The only significant relationship that isn’t immediately obvious as to why the P-value is so significant is WinRatio to MoveDistance. With Kills Pg to DamagePg, given enough damage, a character will ‘die’ and that player is out of the competition for first place, meaning that if a person has a large value in Kills per game, they must have a large value in damage per game. But it looks like there is a strong correlation between Win ratio and Move Distance per game, meaing that those players that are able to survive and move around are much more likely to win more and get a better rating.

## 
## Call:
## lm(formula = Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + 
##     Log.solo_RoundsPlayed.nrm.c + Sqrt.solo_DamagePg.nrm.c + 
##     Sqrt.solo_MoveDistancePg.nrm.c + solo_AvgSurvivalTime.nrm.c + 
##     Win.Kills + Win.Damage + Win.Move + Rounds.Damage + Kills.Damage + 
##     Kills.Move + Damage.Move + Time.Move)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45823 -0.04345  0.00304  0.05031  0.29843 
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     0.650697   0.001165 558.417  < 2e-16 ***
## Log.solo_WinRatio.nrm.c         0.020085   0.001704  11.787  < 2e-16 ***
## Log.solo_RoundsPlayed.nrm.c     0.121051   0.001234  98.087  < 2e-16 ***
## Sqrt.solo_DamagePg.nrm.c        0.337547   0.018143  18.605  < 2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm.c  0.401127   0.013396  29.943  < 2e-16 ***
## solo_AvgSurvivalTime.nrm.c      0.111336   0.010468  10.636  < 2e-16 ***
## Win.Kills                      -0.018297   0.006918  -2.645  0.00820 ** 
## Win.Damage                      0.209453   0.047977   4.366 1.29e-05 ***
## Win.Move                       -0.065846   0.014909  -4.417 1.02e-05 ***
## Rounds.Damage                  -0.033661   0.013333  -2.525  0.01161 *  
## Kills.Damage                   -0.329517   0.027429 -12.013  < 2e-16 ***
## Kills.Move                     -0.360068   0.089397  -4.028 5.69e-05 ***
## Damage.Move                     1.426012   0.492683   2.894  0.00381 ** 
## Time.Move                      -0.404073   0.091906  -4.397 1.12e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07147 on 6932 degrees of freedom
## Multiple R-squared:  0.7058, Adjusted R-squared:  0.7052 
## F-statistic:  1279 on 13 and 6932 DF,  p-value: < 2.2e-16
## Analysis of Variance Table
## 
## Model 1: Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move + 
##     Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move + 
##     Time.Move
## Model 2: Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c + 
##     Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c + 
##     solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move + 
##     Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move + 
##     Time.Move
##   Res.Df    RSS Df Sum of Sq F Pr(>F)
## 1   6932 35.413                      
## 2   6932 35.413  0         0

Difference between models have a p-value of 0.

# All the plots for the reduced stepwise model look nice, with a few outliers, none outside the cook’s distance.There is one standardized residual that has an absolute value greater than 4.

## Warning in par(mfrom = c(1, 2)): "mfrom" is not a graphical parameter
## Warning: package 'car' was built under R version 3.4.3

## [1] 0.08978972

##        Log.solo_WinRatio.nrm.c    Log.solo_RoundsPlayed.nrm.c 
##                       4.347732                       2.764840 
##       Sqrt.solo_DamagePg.nrm.c Sqrt.solo_MoveDistancePg.nrm.c 
##                       3.109261                       2.007873 
##     solo_AvgSurvivalTime.nrm.c                      Win.Kills 
##                       2.139084                      27.018522 
##                     Win.Damage                       Win.Move 
##                      47.445147                       3.509912 
##                  Rounds.Damage                   Kills.Damage 
##                       4.803084                       5.582264 
##                     Kills.Move                    Damage.Move 
##                      27.635295                      30.185092 
##                      Time.Move 
##                       2.119333
## [1] 12.51288

The variance inflation factors range from 2 to 47.45. The latter being for Win Ratio and Damage. The VIF is greater than 10 for Win.Kills, Win.Damage, Kills.Move, Damage.Move. With a mean of 12.51.

## 
## Call:
## lm(formula = Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + 
##     Log.solo_RoundsPlayed.nrm.c + Sqrt.solo_DamagePg.nrm.c + 
##     Sqrt.solo_MoveDistancePg.nrm.c + solo_AvgSurvivalTime.nrm.c + 
##     Win.Kills + Win.Damage + Win.Move + Rounds.Damage + Kills.Damage + 
##     Kills.Move + Damage.Move + Time.Move)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.45823 -0.04345  0.00304  0.05031  0.29843 
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     0.650697   0.001165 558.417  < 2e-16 ***
## Log.solo_WinRatio.nrm.c         0.020085   0.001704  11.787  < 2e-16 ***
## Log.solo_RoundsPlayed.nrm.c     0.121051   0.001234  98.087  < 2e-16 ***
## Sqrt.solo_DamagePg.nrm.c        0.337547   0.018143  18.605  < 2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm.c  0.401127   0.013396  29.943  < 2e-16 ***
## solo_AvgSurvivalTime.nrm.c      0.111336   0.010468  10.636  < 2e-16 ***
## Win.Kills                      -0.018297   0.006918  -2.645  0.00820 ** 
## Win.Damage                      0.209453   0.047977   4.366 1.29e-05 ***
## Win.Move                       -0.065846   0.014909  -4.417 1.02e-05 ***
## Rounds.Damage                  -0.033661   0.013333  -2.525  0.01161 *  
## Kills.Damage                   -0.329517   0.027429 -12.013  < 2e-16 ***
## Kills.Move                     -0.360068   0.089397  -4.028 5.69e-05 ***
## Damage.Move                     1.426012   0.492683   2.894  0.00381 ** 
## Time.Move                      -0.404073   0.091906  -4.397 1.12e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07147 on 6932 degrees of freedom
## Multiple R-squared:  0.7058, Adjusted R-squared:  0.7052 
## F-statistic:  1279 on 13 and 6932 DF,  p-value: < 2.2e-16

From this final model we can see the effect that each predictor has on increasing our response variable solo rating. The predictor with the largest estimate is solo_moveDistancePg, and solo_DamagePg. Meaing that if a player wants to increase their solo rating in PUBG they should move around the arena a lot in search of more gear and more enemies to fight. Since KillsPg and DamagePg are so highly correlated, the removal of one of those predictors does not harm the model greatly. Although survival is the ultimate goal of every PUBG game, this does not mean that a player should sit tight and wait until the rest of the players fight each other. To get a better rating most effectively, a player should work on effectivley manuvering the arena and become proficint in player to player combat.

Final residual standard eror is 0.07, and final Adjusted R^2 of .7052, an improvement of .306 for our Adjusted R-squared from the first order model.